Munich Personal RePEc Archive
Peer Group Effects on the Academic
Performance of Italian Students
De Paola, Maria and Scoppa, Vincenzo
Department of Economics and Statistics, University of Calabria
(Italy)
January 2009
Online at
https://mpra.ub.uni-muenchen.de/18428/
1
Peer Group Effects on the Academic Performance
of Italian Students
Maria De Paola and Vincenzo Scoppa*
Working Paper Version
Forthcoming in Applied Economics, 2010
Abstract. We analyse peer effects among students of a middle-sized Italian public university. We explain students’ average grade in exams passed during their Second Level Degree course on the basis of their pre-determined measures of abilities, personal characteristics and peer group abilities. Thanks to a rich administrative dataset, we are able to build a variety of definitions of peer groups, describing different kinds of students’ interaction, based on classes attended together or exams taken in the same session. Self-selection problems are handled through Two-Stage Least Squares estimations using as an instrument, the exogenous assigning of students to different teaching classes in the compulsory courses attended during their First Level Degree course. We find statistically significant positive peer group effects, which are robust to the different definitions of peer group and to different measures of abilities.
JEL Classification: I21; Z13; J24.
1. Introduction
Educational economists have highlighted, in theoretical and empirical studies, the relevance of
peer group quality to student performance (Epple and Romano, 1998; Hoxby, 2000). A peer
group affects student achievement in several ways: members of a group interact in learning,
help each other in their studies, share important information, impose externalities on others by
behaving well or badly (for example, a noisy student disrupts the study environment) or by
allowing teachers to go deeper in subjects, contribute to the formation of values and aspirations,
and so on.
Understanding the nature and the magnitude of peer group effects in education is crucial
for the “productivity” of educational processes and the organizational design of school systems.
For example, in order to improve student outcomes, it is important to know which inputs
influence their performance most and the relative importance of peer effects compared to other
inputs, such as teacher quality or school resources. Peer effects are also important in school
*
2
design. If peer effects are at work, educational outcomes are affected by how students are
arranged across classes and the desirability of comprehensive schools (which mix students of
different abilities together) or stratified schools (which tend to aggregate students according to
their abilities) depends on the magnitude and non-linearity of peer effects. Further more, the
selectivity of university admission policies produces different results in the presence of peer
effects. More importantly, the nature of peer effects also has fundamental implications in a
family’s choice with regards whether parents consider that their offspring would benefit from
schools which sort students according to their abilities.
Starting from the classical study of Coleman et al. (1966), a host of works have
analysed the effects of peer group on children’s achievement and educational outcomes (Betts
and Morell, 1999; Hoxby, 2000; Angrist and Lang, 2004; Hanushek et al., 2003) and on college
students’ grades and choices of fields of study (Sacerdote, 2001; Zimmerman, 2003; De Giorgi,
Pellizzari and Redaelli, 2006; Foster, 2006), but several problems and controversies are still
unresolved. Some of these studies show that peer effects are statistically and economically
significant in a variety of educational contexts and that students tend to perform better if the
quality of their peer group is higher (Ding and Lehrer, 2006; Zimmerman 2003; Vandenberghe,
2002; Hoxby, 2000; Sacerdote, 2001; Zimmer and Toma, 2000). Moreover, a number of these
studies show that peer effects are often non-linear, implying that students of middle abilities are
particularly affected by the negative influence of weak students (Sacerdote, 2001; Zimmerman,
2003). However, the significance and size of peer effects often changes in relation to the sample
used. Other studies, in fact, find no significant (or minor) peer effects (Angrist and Lang, 2004;
Arcidiacono and Nicholson, 2005; Foster, 2006).
Earlier analyses of peer effects were based on simple econometric models regressing
students outcomes on their own individual characteristics (measures of ability, family
background and so on) and on their peers’ outcomes or characteristics.
As shown by Manski (1993), this kind of regression is plagued by two main
econometric problems, which raise doubts about the causal interpretation of the coefficient
measuring peer group effects. The first problem, known as “self-selection” bias, depends on the
fact that groups of peers are often not exogenously determined, but individuals typically choose
the other people they will associate with . Therefore, the characteristics of each student
contribute to determining the choice of his/her peers and, if some of these characteristics are not
observable, an endogeneity problem arises.
The second econometric problem, known as the “reflection” problem, emerges because
the outcomes of students in a peer group evolve in an interdependent manner: the achievements
of each member affects the achievements of other members but, at the same time, is, itself,
affected by the achievements of those self-same peers. Therefore, an estimation bias emerges,
3
Recent empirical studies have undertaken a variety of estimation strategies to handle
these problems. A strategy used by a number of researchers is that of relying on some sort of
natural experiment which brings about random assignment of peers. Sacerdote (2001),
Zimmerman (2003) and Foster (2006) analyse peer group effects among undergraduate students
who are randomly assigned to a college residence. Recently, De Giorgi, Pellizzari and Redaelli
(2006) have used random assignment to teaching classes as identification strategy to estimate
peer effects on the choice of the field of study. Other works rely on instrumental variables to
remove the correlation between unobserved characteristics and peer characteristics trying to find
exogenous determinants of peer quality (Evans, Oates and Schwab, 1992; Case and Katz, 1991).
A number of papers try to take into account the endogeneity of the peer group by controlling for
school and individual fixed effects (Arcidiacono and Nicholson, 2004; Hanushek et al., 2003).
Most of the works on peer effects among college students use data from (highly
selective) US universities, whereas few works have analysed peer effects in European
universities. Our analysis is an attempt to reduce this gap by providing evidence of peer effects
among students of a middle sized Italian university located in the South of the country.
Importantly, while most of the work on peer effects in tertiary education considers residential
peer groups emerging among roommates, we are able to analyze the effects produced on student
performance by interaction among students who share the same teaching environment and study
together.
Thanks to a rich administrative dataset of students enrolled in the Second Level Degree
(“Laurea Specialistica”)1course in Business Administration at the University of Calabria, we are
able to build different definitions of the peer groups, mainly based on students attending classes
together and sitting their exams in the same session. This allows us to investigate peer group
effects which operate among classmates through mechanisms which rely on the fact that
classmates contribute to the shaping of their educational environment and that students typically
interact and establish friendly relationships with students attending lectures in the same classes.
Classmates with high abilities help create a more effective learning process: instructors
are not interrupted by students asking silly questions and are able to use more challenging
material, in addition they are encouraged in their teaching activity by interested and clever
students etc. (see Lazear, 2001). We consider this kind of effect through a measure of a peer
group based on students attending courses together. For each student i we consider, as members
of his/her peer group, those students who have taken courses together with i. Peer group quality
is then calculated as the weighted average of abilities of students in the group, using the number
of courses taken together as weights.
Apart from peer effects related to the classroom environment, students belonging to the
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4
same class tend to study and revise the subject together, so generating important externalities.
Clearly friendly relationships do not involve all members of a class: some students might attend
a course together, but their interaction might still be limited. We are able to address this
problem by considering a measure of peer group which weights peers in relation to the number
of exams taken together. In fact, students who continually do exams in the same session as one
another are often students who study together, sharing course material and information. We look
at all the students passing an exam on the same date and we use this information to define a
second measure of peer group quality, which weights the abilities of each student according to
the number of exams taken together with student i.2
We are aware that these definitions may be affected by self-selection problems since
students choose other people to collaborate with in studying. In order to overcome possible
self-selection problems, we use a Two-Stage Least Squares estimation and instrument peer groups
through the random (and compulsory) assignment of students to different teaching classes
during their First Level Degree course (for a similar strategy, see Foster, 2006).
Our estimations show that peer group abilities have considerable, positive effects on
students’ academic performance. These effects are not brought about by self-selection and are
robust to a variety of definitions of peer group and several measures of abilities. In our preferred
Instrumental Variable specification, we find that an increase of one standard deviation in peer
group quality (measured as the average ability of students attending the same course) produces
an increase in student performance of 0.19 (the OLS estimates show a smaller effect equal to
0.13). This is quite a large effect, since the effect produced by an increase of one standard
deviation in the student’s own ability generates an increase of 0.54. Effects are slightly higher
when we consider our second measure of peer group quality, based on repeated interaction at
exams, implying that this measure is able to take into account some relevant interaction taking
place among students.
These results suggest that student quality is an important input in tertiary education and
that, in order to improve their students’ performance, colleges and university should attract high
quality students. Our results are consistent with selection policies adopted by many US
universities aimed at admitting only the best students. They also support the idea that students
applying for highly reputable institutions evaluate not only the high quality of instructors
provided, but also the high-quality of peers. Moreover, if student performance is determined, at
least in part, by his/her effort then is rational to subsidize good students for the positive
externalities they produce.
This paper is organized in the following way. In section 2, data are presented and some
descriptive statistics are offered. In section 3, we estimate a simple OLS model. In section 4, we
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5
instrument our measures of peer group by using the exogenous assignment of students to
different teaching classes as an instrument. Section 5 concludes.
2. Data and Descriptive Statistics
Our analysis is based on administrative data from the University of Calabria, a middle-sized
public university located in the South of Italy. It has currently about 31,000 students enrolled in
different degree courses and at different levels of the Italian University system, which, since the
University Reform of 2001, is organized around two main levels, comprised of First Level
Degrees (3 years legal duration) and Second Level Degrees (2 years). Students who have
acquired a First Level Degree can undertake a Second Level Degree.3 In order to gain a Second
Level Degree students have to pass about 20 exams and to write a dissertation, obtaining a total
of 120 credits.4
We focus our analysis on students enrolled, for the academic years 2004-2005 and
2005-2006, on the Second Level Degree course in “Business Administration” (“Laurea
Specialistica in Economia Aziendale”). The administrative data we have at hand provide
detailed information on students’ personal characteristics, secondary school and academic
results, gender, type of High school attended and final High school grade, province of
residence5, grades obtained on each course and date of each exam, grades obtained in the First
Level Degree course, and initial year of enrolment.6
We started with a sample of 267 students, but we excluded students who had done
fewer than 3 exams and, to render students enrolled in different years comparable, we only
considered exams taken in the first year of their Second Level Degree. Moreover, since, in our
analysis, we use information about the academic career of students who have acquired their
First Level Degree at the University of Calabria, we excluded some observations and our final
sample was composed of 212 students.
Table 1 provides descriptive statistics for the sample of students we use. During the first
year of the Second Level Degree course, our sample of students passed an average of 7.71
exams per student. Grades range from 18 to 30 and “30 cum laude”, which we consider equal to
31. The Average Grade over the exams taken by each student is the measure of academic
performance which we use as a dependent variable. The mean of Average Grade is 27.05 and its
standard deviation is 2.06.
About sixty percent of the students were female. 76 students (36%) were enrolled in
their second year and 136 in their first. Students mainly came from two different types of High
school: Lyceums (about 34%) and Technical and Vocational Schools (about 66%). Final High
3
After Second Level Degree students can enrol in a Ph.D degree.
4
Each course typically gives 5 credits.
5
Provinces correspond to the Nuts 3 Eurostat classification.
6
6
school Grade (which we denote throughout the paper as AbilityHS) ranges from 60 to 100, with
a mean of 89.17. The average grade they obtained at exams during their First Level Degree
(denoted as AbilityFirst) is 25.58. The Final First Degree Grade ranges from 86 to 110 and
“110 cum laude” (which we set as equal to 111) and has a mean of 102.96.7
In order to define a single index of individual ability (denoted as Ability), we undertook
a principal component analysis summarizing the different measures of ability which we had
available (AbilityHS, AbilityFirst, Final First Degree Grade, a dummy for the type of High
School denoted as Lyceum)8. Principal component analysis creates linear combinations of the
original variables which capture the greatest variance. We only use the first principal
[image:7.595.84.507.306.411.2]component.
Table 1. Descriptive statistics for the sample of students enrolled on the Second Level Degree course in Business Administration
Variables Mean Std. Dev Min. Max. Obs.
Average Grade in exams 27.046 2.062 19.667 30.6 212
Number of exams passed 7.707 2.592 3 13 212
Female 0.618 0.487 0 1 212
Year of enrolment 0.358 0.481 0 1 212
Final First Level Degree Grade 102.962 6.762 86 111 212
Average Grade in First Level exams (AbilityFirst) 25.579 1.710 21.682 29.472 212
High School Final Grade (AbilityHS) 89.171 11.387 60 100 212
High School Type: Lyceum 0.340 0.475 0 1 212
Ability -0.123 1 -2.291 1.915 212
Notes: Grades in each course ranges from 18 to “30 cum laude” (set equal to 31). Final High School Grade ranges from 60 to 100. Final First Level Degree Grade ranges from 66 to “110 cum laude” (set equal to 111).
3. Econometric Estimations of Peer Group Effects
We analyse the influence of peer groups on academic performance assuming that a student’s
academic performance is determined by his/her own characteristics and by the performance and
characteristics of his/her peers (Sacerdote, 2001). Therefore, we start from the following simple
model:
[1] Yi =α+βXi+φXj+γYj+ψzij+εi
where Yi is the performance of student i, Xi is a vector of individual characteristics of i
(measures of his/her ability and personal characteristics), Xj includes the (predetermined)
characteristics of j, belonging to the peer group of i (“contextual effects” in the definition of
Manski, 1993) and Yj are the outcome of i’s peer (Manski’s “endogenous effect”), zij are
common (unobservable) characteristics of the peer group including student i (“correlated
effects”), εi is an error term.
7
The Final First Level Degree Grade is calculated on the basis of the average grade obtained at exams. In our regressions, we prefer to use AbilityFirst because the Final Grade compresses variability (typically each student with an average grade of 27.5 or more obtains the maximum final grade, “110 cum laude”).
8
7
As mentioned previously, this model faces two main econometric problems:
“reflection” and “selection” bias. With regards the “reflection” problem, that is the fact that the
achievement of student i, Yi, is determined by the performance of his/her peers, Yj, but,
simultaneously, Yj is determined by Yi, we follow the literature (see Sacerdote, 2001;
Ammermueller and Pischke, 2006), and considering an equation symmetric to [1] for the
performance of each student j in i’s peer group , by substitution, we obtain the following
reduced form equation:
(
)
(
2)
(
(
2)
)
(
(
2)
)
(
)
(
1(
2)
)
1 1
1 1
1
γ ε γε ψ γ γ
γβ φ γ
γφ β γ
γ α
− + + +
+ −
+ + −
+ + −
+
= ij j i
j i
i
z X
X Y
or, more simply:
[2] Yi=α~+β~Xi+φ~Xj+ε~
By estimating equation [2], we are therefore unable to recover the structural parameter
φ and γ and distinguish “endogenous” from “contextual” peer effects, but, in equation [2], we
obtain the magnitude of “total peer effects” φ~, which is what matters from a policy point of
view, although it may be unsatisfactory from a theoretical perspective.
Another important problem, which may lead to a biased and inconsistent estimate of φ~
using OLS, is the endogeneity of Xj, due to the fact that individuals typically select people
with whom to associate. This clearly contrasts with an ideal situation in which individuals are
randomly assigned to different peer groups. If peers are selected according to individual
characteristics that affect his/her own level of attainment (but are unobservable to the
researcher), we may end up considering as a peer effect something that, instead, depends on the
individual’s own attributes which are captured through his/her peer group quality.
This issue is particularly relevant for our analysis, since our peer group measures are
based on students taking common courses and exams: students with similar characteristics are
likely to choose the same courses or to sit a particular exam in the same session. We tackle this
problem by using, as an instrumental variable for peer group quality, the random assignment of
students to teaching classes, which, we believe, influences peer group formation, but is not
correlated to the error term ~ , and estimating with the classical Two-Stage Least Squares zij
(Evans, Oates and Schwab, 1992).
We first estimate a single-equation model with Ordinary Least Squares (OLS) assuming
that peer group quality is exogenous. In the next Section, we extend the model to deal with the
endogeneity problem, treating peer group as a choice variable.
Our dependent variable Yi is the Average Grade in exams taken by student i during
8
measures are considered of i’s own ability: Final High School Grade (AbilityHS), Average
Grade in the First Level Degree course (AbilityFirst), and a composite index of individual
ability (Ability)). Other personal characteristics included in vector Xi are: a gender dummy
(Female), a dummy for the type of High School (Lyceum), and dummies for province of
residence.
In order to take into account the levels of difficulty of the different courses chosen by
each student (or different evaluation criteria used by different lecturers),9 we control, in each
regression, for the average of the grades (Average Course Grade) obtained by all other students
taking a given exam and consider the average over all of the exams taken by student i. Since, as
we explain below, our sample students have attended part of their First Level Degree courses in
different teaching classes, we control for some quality characteristics of the instructors teaching
in each classes which may affect students’ performance, such as research activity (Instructors’
Publications) and teaching experience (Instructors’ Experience). As these regressors vary at
teaching classes level, in order to avoid biased standard errors, we estimate our models
clustering the standard errors at this level (Moulton, 1990).
All variables have been standardized in order to make results comparable in different
specifications and to render the interpretation of marginal effects more straightforward.
In Table 2, we report estimates of alternative specifications of our model. In all
specifications, standard errors (reported in parentheses) are corrected for heteroskedasticity. All
equations include province of residence dummies (not reported so as to save space).
In column 1, we first estimate an equation without peer effects to check which factors
determine academic performance. We show that AbilityFirst greatly explains our dependent
variable, while AbilityHS is not significant.10 Average Course Grade is positive and highly
significant. The Female and Lyceum dummies are not significant, nor are the dummies for
province of residence. Variables measuring teaching quality on the First Level Degree courses
show a positive and statistically significant effect.
The other columns in Table 2 include peer group quality among explanatory variables.
We use different measures of peer group quality. From a theoretical point of view, it is not clear
whether a student is influenced mainly by his/her close friends, or by his/her classmates, or by
his/her roommates in college, or by people from his/her place of residence. Our definitions of
peer group are at an aggregate level and tend to describe different types of interaction among
students.
Our first definition of peer group (Peer Course) is based on the group of students who
9
Students have a certain freedom to choose courses in their Degree program, after some compulsory courses.
10
9
have taken a given course, attending classes and taking the exam in the same academic year.
Therefore, in this case, we are assuming that the relevant peer group is represented by people
who attend classes together. As shown by Lazear (2001), education in a classroom environment
is almost a public good. Weak students may impose negative externalities on other students by
disturbing or slowing-down learning and viceversa.
Students on the Second Level Degree course in Business and Administration at the
University of Calabria enrol in a wide range of courses. We do not observe directly the
composition of students on each course, but we infer this information from exams taken by
students in a given year.
For each exam k taken by student i, we first determine the average ability (using
different measures: AbilityHS, AbilityFirst and Ability) of all other students taking the same
course. Then, we take the average over all the exams taken by i to calculate the ability of i’s
peer group:
∑ ∑
= = ⎟
⎟ ⎠ ⎞ ⎜
⎜ ⎝ ⎛
= i k
N
k
J
j j k i
i A
J N Course Peer
1 1
1 1
where Aj is the ability of j, Jk is the number of peers in the exam k, Ni are the exams taken by i.
The average number of exams taken by each students is 7.7111, while the average number of
students in each course is 24.82.
Columns 2, 3 and 4 of Table 2 use AbilityHS, AbilityFirst and Ability respectively as a
measure of peer ability Aj. In all specifications, controlling for individual characteristics and
teaching quality, peer effects appear positive and significant. An increase in the
(pre-determined) ability of the peer group of student i (whichever way it is measured) leads to an
improvement in the academic performance of i. For example, as shown in column 4, an increase
in the ability of the peer group (measured as Ability) of one standard deviation leads to an
improvent in student performance of about 0.13. The coefficient is significant at 5 percent
level.
Smaller effects emerge when we measure peer group ability on the basis of final High
School grade or of average grade during the First Level degree course (respectively AbilityHS
and AbilityFirst). As it is possible to see in columns 2 and 3, the coefficient is in, both
cases,about 0.06, significant respectively at 10 and 5 percent level.
The other explanatory variables have approximately the same level of significance as in
column 1. Student’s own abilities, measured by the average grade during the First Level Degree
course (or by Ability), is, in each specification, positive and highly significant. An increase of
one standard deviation of an individual’s own ability improves performance by about 0.55.
Average Course Grade is always significant, implying that courses chosen by students have
11
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different degrees of difficulty. Our variables explain more than 50% of total variability.
In column 5, we investigate the existence of non-linearity in peer effects. Using Ability,
we have created two dummy variables for whether or not peer group quality was in the top 25
percent (Peer Course Top), or in the middle 50 percent of the distribution (Peer Course
Middle). The bottom 25 percent (Peer Course Bottom) represents the omitted category. As
shown in column 5, students are positively affected by having a peer group of high and medium
quality (statistically significant respectively at 5 and 1 percent level). The magnitude of
coefficients is very similar, implying that having a peer group of medium ability instead of one
of high ability does not produce any relevant change in student performance. Results do not
change when using different measures of ability.
Following Betts and Morell (1999), in column 6, we also verify whether
socio-economic characteristics of the community where students come from influence their
performance. We introduce an indicator of educational level, measured as the percentage of
people living in the area (town or city) where student i is resident with a college or a high
school diploma (Population with College or HS), average income (Income), and the
unemployment rate in the area (Unemployment).12 These socio-economic characteristics do not
seem to play a relevant role in shaping students’ performance, since their coefficients are all not
statistically significant.
12
11
Table 2. OLS regression estimates for academic achievement.
Dependent variable: Average Grade in Second Level Degree course exams
Explanatory Variables 1 2 3 4 5 6
AbilityFirst 0.565***
[0.062] 0.545*** [0.058] 0.541*** [0.056] 0.539*** [0.069]
AbilityHS 0.074
[0.044] 0.082 [0.047] 0.085 [0.043] 0.092* [0.043]
Ability 0.554***
[0.051]
0.558***
[0.051]
Female 0.004
[0.038] -0.009 [0.043] -0.015 [0.044] -0.117 [0.067] -0.133 [0.101] -0.009 [0.051]
Lyceum -0.003
[0.106] 0.004 [0.103] 0.006 [0.102] 0.001 [0.111]
Average Course Grade 0.357***
[0.027] 0.344*** [0.029] 0.353*** [0.027] 0.326*** [0.027] 0.304*** [0.048] 0.339*** [0.022] Instructors’ Publications 0.326**
[0.099] 0.276** [0.082] 0.233** [0.083] 0.234 [0.119] 0.344* [0.201] 0.226* [0.096] Instructors’ Experience 0.375**
[0.112] 0.310** [0.097] 0.259* [0.102] 0.236 [0.139] 0.363* [0.204] 0.256* [0.102]
Peer Course (AbilityHS) 0.059*
[0.026]
0.064* [0.026]
Peer Course (AbilityFirst) 0.065**
[0.023]
Peer Course (Ability) 0.131**
[0.390]
0.558*** [0.051]
Peer Course Middle 0.347***
[0.132]
Peer Course Top 0.330**
[0.163]
Income -0.028
[0.048]
Population with College or HS -0.001
[0.060]
Unemployment rate -0.079
[0.042]
Constant -0.146
[0.092] -0.146 [0.085] -0.138 [0.091] -0.108 [0.101] -0.412** [0.185] -0.171** [0.057]
Adjusted R2 0.568 0.569 0.569 0.535 0.569
Observations 212 212 212 212 212
Notes: In all regression dummies are included for province of residence. Standard errors, corrected for heteroskedasticity and adjusted for potential clustering at teaching classes level, are reported in brackets. The symbols ***, **, * indicate that coefficients are statistically significant, respectively, at 1, 5, and 10 percent level.
4. Instrumental Variable Estimations
In OLS estimates in Table 2, we assumed that peer group quality is an exogenous variable.
However, individuals typically choose with whom they will associate and so peer quality is, to
some extent, endogenous. In this case, a regression of student performance on peer abilities
would be biased and inconsistent because of an endogeneity problem. Therefore we have to deal
with this problem in order to measure the relevance of peer effects consistently, identifying
cases where the peers were assigned essentially randomly (see Evans, Oates and Schwab, 1992;
Foster, 2006).
We need to find an instrumental variable Z which must comply with the two usual
conditions:
1) the instrument must be correlated with the endogenous variable, that is
(
PeerCourse,Z)
≠0Cov ;
12
reasons other than its influence on the formation of peer groups. It is required that the
instrument is exogenous, that is Cov
( )
Z,ε =0;We believe that our second definition of peer group (Peer First Degree) has these
characteristics. Peer First Degree is based on the classes attended by students in the first years
of their First Level Degree course. Students in our sample were already enrolled at the
University of Calabria for their First Level Degree. As a result of the high number of students
enrolled in the First Level Degree course in Business Administration (about 600 students), they
were assigned to three different teaching classes (Class 1, 2 and 3) for each compulsory course
in the first two years on the alphabetic basis of the initial letter of their surnames. Students were
required to attend lectures in their designated teaching classes and, moreover, it was in the
student’s interest to respect this arrangement, because final exams were laid out autonomously
by the lecturers teaching each class (notwithstanding common programmes). For each year, we
consider as peers all the students attending the same compulsory course as part of the same
assigned classes13 and calculate peer group quality as the average ability of these students (using
our three measures of ability).
This definition of peer group, Peer First Degree, is likely to determine the quality of
peers on the Second Level Degree course since the repeated interactions taking place among
students in these classes are relevant to the defining of their peer group composition: students
typically tend to associate, make friends, form stable groups and continue studying over the
following years with people who attend the same classes, even during their Second Level
Degree course.14 Therefore, Cov
(
PeerCourse,PeerFirstDegree)
≠0. Obviously, this aspect canbe empirically tested and, as we show below, the coefficient of the instrumental variable Peer
First Degree in the first-stage regressions is always highly significant and the F-test used to
verify that our instrument is not weak is highly supportive.
With regards to exogeneity, the Peer First Degree variable is likely to be exogenous
given the random assigning to classes according to alphabetical order and the stringent
requirements for students to attend these classes.
Moreover, belonging to a given teaching classes should not determine a student’s
academic performance (except through its influence on the composition of peer groups), since,
except for instructors’ quality characteristics, for which we control, resources devoted to
different teaching classes are the same and the same institutional structure was valid over the
two years. For these reasons, we are confident that Cov
(
PeerFirstDegree,ε)
=0First of all, in order to check that our instrument is not “weak”, we have tested whether
the instrument in the first stage regression is significantly different from zero. In the first-stage
regression in which the endogenous variable, Peer Course, is regressed on the instrument, Peer
13
The average number of peers according to this definition is 40.83.
14
13
First Class, and all other exogenous variables, the F-statistics, for the test of whether the
instrument coefficient is equal to zero, are always well above the threshold value of 10
suggested by Stock and Watson (2003) (F-statistics range from 33 to 140 according to different
measures of abilities used).
As a further check that the instrument is not weak, as suggested by Angrist and Krueger
(1999), in Table 3, we report results from three different estimates of the reduced-form equation
in which the dependent variable is regressed on all the exogenous variables and on the
instrumental variable, Peer First Degree: in column 1, we use AbilityHS as a measure of peer
ability, in column 2, we use AbilityFirst and, finally, in column 3, we measure ability using the
comprehensive index Ability. Peer First Degree is highly significant in all the specifications,
implying both that our instrumental variable is a strong determinant of peer group quality and
that the peer group influences a student’s academic performance. Instructors’ seniority and
research productivity (measured respectively as the number of years an instructor has worked in
the university system in a permanent position and as the number of published articles in referred
[image:14.595.88.449.432.692.2]journals per year) are not statistically significant.
Table 3. Reduced form equation estimates of academic achievement. Dependent variable: Average Grade in Second Level Degree course exams
Explanatory Variables 1 2 3
AbilityFirst 0.549***
[0.049]
0.548*** [0.054]
AbilityHS 0.079*
[0.039]
0.084* [0.042]
Ability 0.566***
[0.057]
Female 0.002
[0.048]
-0.006 [0.040
-0.111 [0.061]
Lyceum 0.001
[0.048]
0.004 [0.104]
Average Course Grade 0.360***
[0.028]
0.360*** [0.028]
0.354*** [0.028]
Peer First Degree (AbilityHS) 0.104***
[0.026]
Peer First Degree (AbilityFirst) 0.053**
[0.018]
Peer First Degree (Ability) 0.146***
[0.018]
Instructors’ seniority 0.087
[0.093]
0.267** [0.077]
0.034 [0.045]
Instructors’ publications 0.072
[0.087]
0.229** [0.058]
0.047 [0.040]
Constant -0.136
[0.091]
-0.138 [0.093]
-0.103 [0.125]
Adjusted R2 0.572 0.568 0.534
Observations 212 212 212
Notes: Dummies are included in all regressions for province of residence. Standard errors, corrected for heteroskedasticity and adjusted for potential clustering at teaching class level, are reported in brackets. The symbols ***, **, * indicate that coefficients are statistically significant, respectively, at 1, 5, and 10 percent levels.
Two-Stage Least Squares
14
academic performance using the Peer First Degree variable as an instrument for peer group
quality.
Before using an instrumental variable estimator, since OLS would be more efficient
than IV under the hypothesis that OLS are consistent, one should check whether it is necessary
to use IV at all. In order to verify this aspect, we run the Durbin-Wu-Hausman test to verify the
endogeneity of Peer Course in OLS. We take the residuals from the first stage regression and
insert them, as explanatory variables, into an “augmented” structural equation. In many of our
specifications, this variable is significantly different from zero (with the exception of the ability
measure “Ability First”) showing that OLS is not consistent and suggesting the use of IV to
address the problem of endogeneity.
Two-Stage Least Squares Estimations results are shown in Table 4. As above, the three
columns use AbilityHS, AbilityFirst and Ability respectively as a measure of peer ability.
Panel B of Table 4 shows the results from First Stage regressions for the different peer
ability measures. In all the specifications, it emerges that Peer First Degree strongly determines
the quality of the peer group as measured by Peer Course. Moreover, peer group quality is also
influenced by a student’s own individual abilities.
Panel A shows Two Stage Least Squares estimations. Peer Course coefficients are
always positive and highly significant, regardless of how ability is measured. In column 1,
controlling for Instructors’ publications and seniority, if peer group quality (measured by
AbilityHS) increases by one standard deviation then a student’s performance improves by
0.24. This coefficient is significant at 10 percent level. In columns 2 and 3, using AbilityFirst
and Ability respectively, an increase of one standard deviation in peer quality leads to an
improvement in student performance of 0.09 and 0.19 respectively (significant at 5 and 1
percent levels).
In general, the IV coefficients are higher than the OLS coefficients. This suggests that
measurement errors in the quality of peer group – which may bias our coefficient of interest
15 Table 4. IV regressions of student’s academic performance
Dependent variable: Average Grade in Second Level Degree course exams
Explanatory Variables 1 2 3 Panel A: Two-Stage Least Squares
AbilityFirst 0.485*** [0.083] 0.530*** [0.051]
AbilityHS 0.106
[0.059]
0.089* [0.042]
Ability 0.541***
[0.055]
Female -0.051
[0.034]
-0.016 [0.050]
-0.123 [0.072]
Average Course Grade 0.306***
[0.033]
0.349*** [0.031]
0.317*** [0.029]
Lyceum 0.022
[0.102]
0.004 [0.103]
Peer Course (AbilityHS) 0.237*
[0.099]
Peer Course (AbilityFirst) 0.089**
[0.027]
Peer Course (Ability) 0.188***
[0.027]
Instructors’ publications 0.124
[0.135]
0.222*** [0.052]
0.163** [0.060]
Instructors’ seniority 0.117
[0.158]
0.240** [0.068]
0.145* [0.067]
Constant -0.146
[0.079]
-0.130 [0.087]
-0.099 [0.101]
Panel B: First Stage Regressions
AbilityFirst 0.268***
[0.700]
0.202*** [0.051]
AbilityHS -0.112
[0.075]
-0.058 [0.053]
Ability 0.133***
[0.047] .
Female 0.224
[0.123]
0.116 [0.086]
0.062 [0.096]
Average Course Grade 0.231***
[0.053]
0.129*** [0.037]
0.194*** [0.043]
Lyceum -0.303
[0.318]
-0.001 [0.081]
Peer First Degree (AbilityHS) 0.436***
[0.075]
Peer First Degree (AbilityFirst) 0.600***
[0.046]
Peer First Degree (Ability) 0.775***
[0.047]
Instructors’ publications -0.220
[0.310]
0.080 [0.192]
-0.616** [0.250]
Instructors’ seniority -0.126
[0.325]
0.303 [0.196]
-0.591** [0.267]
Adjusted R2 0.367 0.679 0.611
Observations 212 212 212
Notes: Panel A reports the Two-Stage Least Squares estimates, instrumenting Peer Course using Peer First Degree. Panel B reports the corresponding first stage. Dummies are included in all regressions for province of residence. Standard errors, corrected for heteroskedasticity and adjusted for potential clustering at teaching class level, are reported in brackets. The symbols ***, **, * indicate that coefficients are statistically significant, respectively, at 1, 5, and 10 percent levels.
Evaluating Peer effects for individuals who study together
Students belonging to the same class tend to study and revise the subject together, so generating
important externalities. However, this kind of relationship does not develop between all the
members of a class, since, even though attending courses together, some students may not
16
(called Peer Exam) based on this type of interaction, which we believe particularly relevant, we
consider as members of the same group students who sit an exam on the same date. Anecdotal
evidence suggests that students who study together tend to take exams together.
In each academic year, students in our sample have 7 different dates available to take a
given exam. For each student, we are able calculate how many times he/she meets any other
students at exams or, more precisely, how many times they passed an exam on the same date.15
Students who meet more often at exams are presumably part of the same group. Therefore, we
calculate the ability of the peer group as a weighted average of “matched” students’ abilities
(with the three measures: AbilityHS, AbilityFirst and Ability), using the number of matches at
exams as weights:
∑
== i
n
j
j ij i
i m A
M PeerExam
1 1
where Aj is the ability of student j, mij is the number of times student i met student j at exams,
i
n is the number of students met by i, and
∑
== i
n
j ij i m M
1
is the total number of matches of i.
This measure of peer group ability weights the ability of each member of the peer group
according to the number of exams taken together: students who are found to have often sat
exams together are given a higher weight, while those who match less frequently are weighted
less.16 A similar strategy to building a peer group is followed by Bayer et al. (2007)17 and De
Giorgi, Pellizzari and Redaelli (2006).
Columns 1, 2 and 3 in Table 5 use Peer Exam, calculated using our alternative measures
of ability, and instrument this variable (which we strongly suspect to be endogenous), again
using Peer First Degree. The Durbin-Wu-Hausman test shows that OLS would not be
consistent (for example, using Ability, the t-statistics of residuals in the augmented structural
regression is equal to 3.12) and support the use of IV to address the problem of endogeneity.
Through this new definition of peer group, our previous results with regards the
relevance of peer effects are confirmed. In fact, the results show that: (a) Peer First Degree
determines the formation of a peer group (as shown by the high significance of the relative
coefficient in first stage regressions and by the test for weak instruments for which F-statistics
takes on values from 26 to 170) and that (b) peer group quality is an important determinant of a
student’s academic performance (regardless of how abilities are measured). In column 1, we
show that if Peer Exam measured using AbilityHS increases by one standard deviation, then a
15
Unfortunately, we have data on passed exams only, as no information is available regards failed exams.
16
We also experimented with a measure of peer group which excludes from the peer group all students sitting together only once or twice (because this meetings could be due to pure chance). Results are similar to those reported.
17
17
student’s academic performance improves by 0.26 (the coefficient is significant at 5 percent
level). Analogous results are obtained if we use alternative measures of peer group abilities. For
example, using Ability, we find that an increase of one standard deviation in the peer group
quality leads to an improvement of 0.28 in the student’s academic performance (significant at a
1 percent level).
These coefficients are slightly higher compared to those obtained by considering all
students attending courses together as peer groups, implying that students’ performance is more
18 Table 5. IV regressions of student’s academic performance
Dependent variable: Average Grade in Second Level Degree course exams
Explanatory Variables 1 2 3 Panel A: Two-Stage Least Squares
AbilityFirst
0.520*** [0.062] 0.534*** [0.056]
AbilityHS 0.051
[0.057]
0.069 [0.051]
Ability 0.494***
[0.075]
Female 0.003
[0.049]
0.002 [0.044]
-0.079 [0.078]
Average Course Grade 0.310***
[0.037]
0.360*** [0.031]
0.313*** [0.036]
Lyceum 0.021
[0.101]
0.004 [0.111]
Peer Exam (AbilityHS) 0.263**
[0.098]
Peer Exam (AbilityFirst) 0.097**
[0.034]
Peer Exam (Ability) 0.282***
[0.045]
Instructors’ publications 0.191
[0.095] 0.248*** [0.048] 0.192*** [0.025] Instructors’ seniority 0.185 [0.113] 0.271*** [0.067] 0.165*** [0.027]
Panel B: First Stage Regressions
AbilityFirst 0.112
[0.072]
0.139*** [0.068]
AbilityHS 0.106
[0.076]
0.153 [0.071]
Ability 0.256***
[0.059]
Female -0.002
[0.125]
-0.080 [0.116]
-0.115 [0.121]
Average Course Grade 0.191***
[0.054]
0.002 [0.050]
0.145** [0.054]
Lyceum -0.077
[0.119]
0.020 [0.058]
Peer First Degree (AbilityHS) 0.394***
[0.077]
Peer First Degree (AbilityFirst) 0.600***
[0.046]
Peer First Degree (Ability) 0.518***
[0.080]
Instructors’ publications -0.453
[0.316]
-0.199 [0.259]
-0.516 [0.314]
Instructors’ seniority -0.374
[0.331]
-0.038 [0.264]
-0.464 [0.335]
Adjusted R2 0.268 0.373 0.377
Observations 212 212 212
Notes: Panel A reports the Two-Stage Least Squares estimates, instrumenting Peer Course using Peer First Degree. Panel B reports the corresponding first stage. Dummies are included in all regressions for province of residence. Standard errors, corrected for heteroskedasticity and adjusted for potential clustering at teaching class level, are reported in brackets. The symbols ***, **, * indicate that coefficients are statistically significant, respectively, at 1, 5, and 10 percent levels.
5. Concluding remarks
A large amount of empirical literature shows that peer group quality has important effects on a
student’s performance and, more in general, on an individual’s results. While, for primary and
secondary education, there is considerable literature analyzing the effects of classmates’ quality
19
effects emerging among roommates and little is known about the effects produced on college
students by different teaching environments.
Thanks to a rich administrative dataset, we are able to build different definitions of the peer
group, mainly based on students attending classes together, interacting in study activity and
sitting their exams in the same session. This allows us to investigate peer group effects which
occur among classmates through mechanisms which rely on the fact that classmates contribute
to the shaping of the educational environment.
In addition, most research on peer group effects in education is focussed on the US,
whereas very few studies examine European schools or universities. To our knowledge, this
paper is the first attempt to evaluate peer effects in an Italian university.18 Moreover, whereas
many papers study highly selective universities with rather homogeneous groups (see Sacerdote,
2001), the students we consider are not sorted through a selection process and are highly
heterogeneous in terms of abilities. This factor, which widens variability, is likely to increase
the relevance of peer effects.
We regress the student’s Average Grade in the Second Level Degree course on his/her
own predetermined characteristics and abilities and on his/her peers’ abilities. We use a variety
of definitions of peer group – based on the courses taken together, on classes attended during
the First Level Degree course, on the dates of exams– and use different measures of abilities
(Final High School Grade, Average First Level Degree Grade, type of High School etc.). It is
likely that the peer group, defined both in terms of classes attended and of exams taken together,
will encompass the relevant interactions among students.
In order to overcome the reflection problem, one of the main econometric problems that
affects estimates of peer effects, we use predetermined variables for abilities, but do not attempt
to distinguish the channels through which peer group influences a student’s performance. From
a policy point of view, this is not particularly detrimental.
The second econometric problem in estimating peer effects is the endogeneity of the
peer group, in that individuals tend to choose people with whom to associate. In order to solve
this issue, we estimate a model with Two-Stage Least Squares, using, as an instrument for peer
group, the teaching classes to which students were assigned within compulsory courses during
their First Level Degree.
Our results show very clearly that peer effects are positive and substantial. Being part
of a group with higher abilities considerably improves a student’s academic performance.
Results are robust to different definitions of a peer group and different measures of ability used.
Peer group effects emerging from our analysis are, in most of the specifications, larger
in magnitude than those shown in other studies (Sacerdote, 2001; Zimmerman, 2003). This
18
20
could be due to the fact that our measure of peer group quality includes interactions among
students – based on attending the same classes, sharing the same educational environment and
studying together – which are likely to be greater than those deriving from sharing the same
accommodation . In fact, people sharing the same room may have limited interaction due to the
fact that they specialise in different areas and have different interests. On the other hand,
students attending the same courses or working together establish relationships that are crucial
in determining effective learning processes.
According to our results, student quality is an important input in tertiary education
implying that attracting high quality students helps colleges and universities to improve their
students’ performance. Positive effects produced by high quality peers are consistent both with
the highly selective policies adopted by many US universities and the high fees that students are
willing to pay to be admitted to these universities.
Peer effects by definition imply positive or negative externalities which lead individual
choices to be different from optimal social choices. If we realistically assume – following the
analysis of Costrell (1994) and Kremer, Miguel and Thorntorn (2007) – that student ability is
not only due to genetic factors, but is also the outcome of student effort during his/her
educational career, our results suggest that high achieving students should be subsidized
(through scholarships and grants) for the positive externalities they produce on other students.
On the other hand, students who perform badly may be encouraged to increase their sub-optimal
level of effort by tuition fees which are inversely related to their academic performance
(Garibaldi et al., 2007).
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